Goncharova O.N.  

Convection under low gravity: models, analytical and numerical investigations

Modeling of the convective processes caused by impact of various
forces on the fluid and gas media is rather important nowadays. The
increased interest to these problems is determined by preparation of
the experiments on the International Space Station. Some of them are
the experiments to investigate the convective flows of the fluids
with a thermocapillary interface between liquid and gas phases.
Mathematical modeling of the various convective processes should be
carried out:  formulation of the problem statements, formulation of
the conditions at the evaporative interface, construction of the
exact solutions in the canonical domains, analytical and numerical
investigation of the simplified problems.

The alternative  mathematical models of convective fluid flows (the
microconvection model of isothermally incompressible liquid, the
model of convection of weakly compressible liquid) and the classical
Oberbeck-Boussinesq model are applicable to investigation of many
problems of convection: convection under low gravity, in small
scales and at fast changes of the boundary thermal regimes.

Principal issues
relating to well/ill posed initial boundary value problems
for the equations of convection are considered.

The examples of the  invariant solutions of the alternative
models of convection
  in an infinite strip are presented.

In the problem of convection of two immiscible  fluids with an
interface  the exact solutions are constructed in the
three-dimensional case.

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